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birds
generative
infseq
renumerable
well_ordered
.gitignore
README.md
birds.rb
fixnum_extensions.rb
generative.rb
generative_gnome.rb
generators.rb
infinite_enumeration.rb
infseq.rb
numfilter.rb
socket_failing_client.rb
socket_failing_server.rb
socket_test.rb
well_ordered.rb

README.md

Code Bucket

Just a dumping area for some random code that pops into my brain.

Sequences

Doing some work on allowing unbounded (but countable) sequences to be handled similarly to other Enumerable collections in Ruby. I've attempted several different approaches found in:

  1. infinite_enumeration.rb (and generators.rb)
  2. infseq.rb
  3. numfilter.rb (and everything in infseq/ directory)
  4. well_ordered.rb (and everything in well_ordered/ directory)

well_ordered.rb is the start of my refactoring. After a days journey through coding, we're starting to arrive at something I like. The name isn't accurrate with regard to the set theoretic definition of wellorder, I'm just not sure what else to call it at this time. To use the WellOrdered module, one need only define the succ and pred instance methods that return the current object's successor and predecessor, respectively. To be able to manipulate things as countably infinite sequences, it may be helpful to use method_missing, or some other delegation method, to hand off unknown messages to a base object. Who knows if this will be useful to anyone, myself included, but it's been a fun exercise so far. This task was started on Ruby 1.8.7, but I have been doing later development of it in Ruby 1.9. I have no intention of testing it against Ruby 1.8.x at this time (though I can almost guarantee that it will not work with 1.8.6 and lower, due to each returning an Enumerator unless a block is provided.) Where possible, I try to let Enumerator/Enumerable do the work for me. Such as with detect, first, and so forth. There are some methods that I don't feel are generally implementable (min, max, etc.) and some that I either can't think of an appropriate analogue for (eg: inject) or haven't bothered to implement yet (drop, drop_while).

Song Birds

The birds directory contains my first few stabs at implementing Raymond Smullyan's song birds (combinators) in terms of Ruby lambda objects. They work, mostly. There is an issue with Y-combinators (Sage birds) and recursion in general due to how I initially handled combinator evaluation and Ruby's evaluation of parameters to a method before invoking the method. In short, a straight-forward attempt at making a Y-combinator from composing two Turing birds results in infinite recursion because the recursion portion of the combinatory expression is evaluated in an unbounded fashion, and the underlying function is never once invoked. I'm working on resolving this now by considering a different approach, though this approach may convince me that Ruby isn't an appropriate place to think about things in terms of combinators.

I believe I've corrected this problem with the new birds.rb file that includes birds/combinators.rb and birds/combinators/bird.rb. For instance:

factorial = U.call(U).call(lambda { |fact|
  lambda { |n| (n==0 && 1) or (n * fact.call(n-1)) }
})

factorial.call(6)
# => 720

If this is now working appropriately, I will be very happy, as there is no language specific tomfoolery being applied to the Y-combinator. It's just as straight forward as U.call(U).call(...) and this excites me!

Alternatively, you could do L.call(O).call(L.call(O)).call(...) or any other Sage bird combinator you like (in fact, this is equivalent to the TuringTuring combinator, perhaps a better example would be S.call(L).call(L).call(...).)

Legal Jazz

All code here was written by Ian D. Eccles unless otherwise noted. Software is released under the Apache License 2.0, unless otherwise noted.